Prof. Dr. Thorsten Jungmann (last updated 2026-10-03)
Maurice Karnaugh (1924–2022) was an American physicist, mathematician, computer scientist and inventor. He studied mathematics and physics at the City College of New York and received his doctorate in physics from Yale University in 1952. From 1952 to 1966 he worked at Bell Labs; he then moved to IBM, first to the Federal Systems Division in Gaithersburg (1966–1970) and from 1970 to the IBM Thomas J. Watson Research Center, where he studied multistage interconnection networks. He also taught computer science at the Polytechnic University of New York, now part of the New York University Tandon School of Engineering.
While at Bell Labs, Karnaugh invented in 1953 a form of logic diagram that provides an alternative technique for representing logic functions: the Karnaugh map (German: Karnaugh-Veitch-Diagramm). His paper ‘The Map Method for Synthesis of Combinational Logic Circuits’ appeared in 1953 in the Transactions of the American Institute of Electrical Engineers. The technique is a refinement of the chart that Veitch had described in 1952, which itself was a rediscovery of Allan Marquand’s logical diagram of 1881; the diagram is also called the Karnaugh–Veitch map.
To use a Karnaugh map, the output values of a logic function are transferred from the truth table onto a two-dimensional grid in which each cell represents one combination of input conditions. The rows and columns are ordered in Gray code, so that only one variable changes between adjacent cells. Groups of 1s or 0s are then identified, and from these groups a minimal sum-of-products or product-of-sums expression can be written. Minimizing by hand with Karnaugh maps is practical only for up to four variables and is not suited for more than six. For more variables the tabular Quine–McCluskey algorithm is more practical, and functions with a large number of variables are minimized with heuristic methods such as the Espresso heuristic logic minimizer.
Reference and further reading:
https://en.wikipedia.org/wiki/Maurice_Karnaugh
https://en.wikipedia.org/wiki/Karnaugh_map
https://en.wikipedia.org/wiki/Quine%E2%80%93McCluskey_algorithm
https://en.wikipedia.org/wiki/Espresso_heuristic_logic_minimizer